Alternative determinism principle for ...
Document type :
Article dans une revue scientifique
Title :
Alternative determinism principle for topological analysis of chaos
Author(s) :
Journal title :
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
Pages :
035202(R)
Publisher :
American Physical Society
Publication date :
2006
ISSN :
1539-3755
English keyword(s) :
chaos
entropy
knots
topology
simplicial spaces
entropy
knots
topology
simplicial spaces
HAL domain(s) :
Science non linéaire [physics]/Dynamique Chaotique [nlin.CD]
English abstract : [en]
The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core ...
Show more >The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon which this approach is built, determinism and continuity, apply in any dimension. We propose an alternative framework in which these principles are enforced on triangulated surfaces rather than curves and show that in dimension three our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.Show less >
Show more >The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon which this approach is built, determinism and continuity, apply in any dimension. We propose an alternative framework in which these principles are enforced on triangulated surfaces rather than curves and show that in dimension three our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Non spécifiée
Popular science :
Non
Source :
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